Chapter 5
Describing, Exploring, and Comparing Data
By Boundless
![Thumbnail](../../../../../figures.boundless-cdn.com/17727/raw/mparison-pythagorean-means.jpg)
The term central tendency relates to the way in which quantitative data tend to cluster around some value.
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The shape of a histogram can assist with identifying other descriptive statistics, such as which measure of central tendency is appropriate to use.
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The root-mean-square, also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity, or set of numbers.
Depending on the characteristic distribution of a data set, the mean, median or mode may be the more appropriate metric for understanding.
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The central tendency for qualitative data can be described via the median or the mode, but not the mean.
![Thumbnail](../../../../../figures.boundless-cdn.com/18491/raw/standard-deviation-diagram.jpg)
Measures of relative standing can be used to compare values from different data sets, or to compare values within the same data set.
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The median is the middle value in distribution when the values are arranged in ascending or descending order.
![Thumbnail](../../../../../figures.boundless-cdn.com/17901/raw/omparison-mean-median-mode.jpg)
The mode is the most commonly occurring value in a distribution.
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The law of averages is a lay term used to express a belief that outcomes of a random event will "even out" within a small sample.
![Thumbnail](../../../../../figures.boundless-cdn.com/17993/raw/random-walk-example.jpg)
A stochastic process is a collection of random variables that is often used to represent the evolution of some random value over time.
![Thumbnail](../../../../../figures.boundless-cdn.com/18085/square/8480394254-572a4dec25-z.jpeg)
The sum of draws is the process of drawing randomly, with replacement, from a set of data and adding up the results.
![Thumbnail](../../../../../figures.boundless-cdn.com/17898/raw/michelsonmorley-boxplot.jpg)
A box plot (also called a box-and-whisker diagram) is a simple visual representation of key features of a univariate sample.
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The sample average/mean can be calculated taking the sum of every piece of data and dividing that sum by the total number of data points.
![Thumbnail](../../../../../figures.boundless-cdn.com/17949/raw/arison-standard-deviations.jpg)
Although they are often used interchangeably, the standard deviation and the standard error are slightly different.
![Thumbnail](../../../../../figures.boundless-cdn.com/17990/raw/standard-deviation-diagram.jpg)
The standard error of the mean is the standard deviation of the sample mean's estimate of a population mean.
![Thumbnail](../../../../../figures.boundless-cdn.com/17991/raw/circuniformdistofmean.jpg)
A stochastic model is used to estimate probability distributions of potential outcomes by allowing for random variation in one or more inputs over time.
The normal (Gaussian) distribution is a commonly used distribution that can be used to display the data in many real life scenarios.
![Thumbnail](../../../../../figures.boundless-cdn.com/17995/raw/student-t-pdf.jpg)
Student's t-test is used in order to compare two independent sample means.
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The odds of an outcome is the ratio of the expected number of times the event will occur to the expected number of times the event will not occur.
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